If f(x) = x^5 - 20x^3 + 240x,then f(x) satisf | vedclass

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(C) Given the function $f(x) = x^5 - 20x^3 + 240x$. To determine the monotonicity,we find the derivative $f'(x)$: $f'(x) = \frac{d}{dx}(x^5 - 20x^3 +

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It is monotonically increasing everywhere

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(C) Given the function $f(x) = x^5 - 20x^3 + 240x$. To determine the monotonicity,we find the derivative $f'(x)$: $f'(x) = \frac{d}{dx}(x^5 - 20x^3 + 240x) = 5x^4 - 60x^2 + 240$. We can factor out $5$: $f'(x) = 5(x^4 - 12x^2 + 48)$. Now,we complete the square for the expression inside the parenthesis: $x^4 - 12x^2 + 48 = (x^2 - 6)^2 - 36 + 48 = (x^2 - 6)^2 + 12$. Thus,$f'(x) = 5[(x^2 - 6)^2 + 12]$. Since $(x^2 - 6)^2 \ge 0$ for all $x \in \mathbb{R}$,it follows that $(x^2 - 6)^2 + 12 \ge 12$. Therefore,$f'(x) \ge 5 	imes 12 = 60 > 0$ for all $x \in \mathbb{R}$. Since $f'(x) > 0$ for all $x$,the function $f(x)$ is monotonically increasing everywhere.

If $f(x) = x^5 - 20x^3 + 240x$,then $f(x)$ satisfies which of the following?

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